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211	MATHEMATICS AND STATISTICS	ABS-280
Normal Form of Periodic FPU Chain with Four Degrees of Freedom and Alternating Masses Stephanus Ardyanto, Johan Matheus Tuwankotta (*) Analysis and Geometry Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung, Indonesia *jmtuwankotta[at]itb.ac.id Abstract In this paper we study the periodic Fermi-Pasta-Ulam (FPU) chain. It is a one dimensional chain of oscillators which endpoints are connected and has nearest-neighbor interaction only. We specify our research by considering the chain with four degrees of freedom and has alternating masses \(1,m,1,m\). Moreover, we also consider a more general potential function in the Hamiltonian function of the system. The analysis is done by using the near identity transformation in phase space. The transformation is defined by using the flow of a linear Hamiltonian system, which is clearly symplectic so that the Hamiltonian structure can be preserved. The transformed Hamiltonian is then called in a so-called Birkhoff-Gustavson normal form. The structure as to the remaining terms in the normal form, depends on the choice of \(a=1/m\). Due to the nature of the problem, there are some discrete symmetries in phase space which simplify the normal form further. Our main focus is to analyze the case when \(a = 1\) (homogeneous chain) and \(a = 3\). Depending on the value of the parameter, the system has topologically nonequivalent phase space which will be classified. The two cases which are considered express two different class of resonances. This is one of the reason why FPU chain is an interesting model to study. Keywords: Periodic FPU chain, alternating masses, Hamiltonian system, normal form Share Link | Plain Format | Corresponding Author (Stephanus Ardyanto)

212	MATHEMATICS AND STATISTICS	ABS-283
Enhanced Detection of Online Loan Fraud using Cost-Sensitive Weighted Random Forest with Recursive Feature Elimination and Cross Validation Karina Agustina, Kartika Fithriasari, Dedy Dwi Prastyo Department of Statistics, Institut Teknologi Sepuluh Nopember, Surabaya 60111, Indonesia karinagustina123[at]gmail.com kartika_f[at]statistika.its.ac.id dedy-dp[at]statistika.its.ac.id Abstract Online loan is one of the innovations that combine credit distribution system with digital technology such that it can be accessed in easy, fast, and efficient ways. The ease of access provided not only encourages the increase in the growth of online loan application from year to year but also increases the risk of fraudulent transactions (fraud). Therefore, a fraud detection system is an essential requirement for credit financial institutions to minimize the risk of losses that may arise. This study compares between Random Forest and Cost-Sensitive Weighted Random Forest model to solve the class imbalance problem in online loan fraud data. Cost-Sensitive Weighted Random Forest is development of Random Forest model that use cost-function based on the misclassification rate of the instances for both majority and minority classes to improve the prediction ability of each tree and the overall performance of the ensemble. The trees are given weightage based on the quantity of error. The trees with lower error rate are given higher weight. This cost driven learning scheme is adapted to give more emphasis on learning the minority class instances. In addition, the Recursive Feature Elimination and Cross Validation method used to eliminate unimportant features biases in the classification results and to speed up the data processing. The proposed methods are tested on real online loan application datasets obtained from a private bank. The results of the study show that information about the device data used when submitting loan application has a considerable influence on decision making to classify the loan application as fraud or not. The findings also show that the Cost-Sensitive Weighted Random Forest works better than Random Forest because it has higher accuracy, F1 score, and AUC-ROC. Keywords: Cost Sensitive Weighted Random Forest, Imbalance Dataset, Fraud Detection Share Link | Plain Format | Corresponding Author (Karina Agustina)

213	MATHEMATICS AND STATISTICS	ABS-30
Effects of Inversion Layer on the Atmospheric Pollutant Dispersion From a High Chimney Fidelis Nofertinus Zai(a), Agus Yodi Gunawan (a*) a) Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology, 40132 Bandung, Indonesia *ayodi[at]itb.ac.id Abstract An inversion layer is a layer in the lower atmosphere at certain height through which there is no transport of pollutants. It plays as a significant factor in the formation of air pollutants where they are trapped. In this paper, a mathematical model describing an atmospheric pollutant dispersion from a high chimney in the presence of an inversion layer is constructed. The aim of the model is to predict the concentration of pollutant at ground level. The concentration of a pollutant released into the air is governed by the advection-diffusion equation. The formulation is made dimensionless. An analytical solution procedure via the integral transforms is presented for the steady state case. Solutions are fully determined by two dimensionless parameters, i.e., the source strength emanating from the chimney and the height of the inversion layer. The pollutant concentration on the ground level with some multiple source formations will be explored, for various values of inversion layer height. Results show that the lower the inversion layer, the higher the pollutant concentration on the ground level is. Keywords: Inversion layer, Dispersion, Advection-diffusion equation, Integral transforms. Share Link | Plain Format | Corresponding Author (Fidelis Nofertinus Zai)

214	MATHEMATICS AND STATISTICS	ABS-31
OPTIMIZATION OF SUPPORT VECTOR REGRESSION PARAMETER BASED ON FIREFLY ALGORITHM AND GENETIC ALGORITHM FOR FORECASTING STOCK PRICES IN CONSTRUCTION AND BUILDING SECTOR Erlyne Nadhilah Widyaningrum, Irhamah, Heri Kuswanto Institut Teknologi Sepuluh Nopember Abstract Stocks are strongly supported by the government and a law has been passed regarding the implementation of activities in the capital market sector. By including capital or stock investment, investors have claims on the assets and income of a company. Stock prices fluctuate and tend to be dynamic at any time, so stock price predictions are needed to maximize profits for investors and avoid losses due to the nature of stock prices. Stock price closing data is generally non-linear, so the SVR (Support Vector Regression) model is used which offers an optimal global solution that works by mapping data to a high-dimensional space and has good performance in solving time series problems and non-linear data. However, to get optimal SVR results, it is necessary to choose parameter values carefully or optimize them so that local optimum values are not obtained, so in this study genetic algorithm optimization and firefly algorithm optimization methods were used in selecting SVR parameters to obtain better forecast results. So, from these calculations, this study found that optimizing the SVR parameters using the genetic algorithm and the firefly algorithm resulted in better forecasting performance. Keywords: Support Vector Regression, Optimization, Firefly Algorithm, Genetic Algorithm Share Link | Plain Format | Corresponding Author (Erlyne Nadhilah Widyaningrum)

215	MATHEMATICS AND STATISTICS	ABS-287
Envelope Computation using Dual Numbers Rizal Afgani KK Analisis dan Geometri, Institut Teknologi Bandung Abstract Using the concept of infinitesimals Anders Kock and others introduced derivative without the notion of limits. Moreover, he introduced the notion of infinitesimal neighbourhood of a point and of family of lines on a plane paramaterized by a curve. He then define the envelope of a given familiy simply as the collection of points of intersections of a line from the family with its neighbours. In this article we show how a concrete computation can be carried out using dual numbers. Keywords: Envelope, Dual Numbers, Share Link | Plain Format | Corresponding Author (Rizal Afgani)

216	MATHEMATICS AND STATISTICS	ABS-32
Primary and Secondary Resonances of a Weakly Nonlinear Oscillator Agus Yodi Gunawan (a*), Farrell Theodore Adriano (b) a) Industrial and Financial Mathematics Research Group, Bandung Institute of Technology Jalan Ganesha 10, Bandung 40132, Indonesia *ayodi[at]math.itb.ac.id b) Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology Jalan Ganesha 10, Bandung 40132, Indonesia *ftheodoreadriano[at]gmail.com Abstract In this paper, a weakly nonlinear forced oscillator having a nonlinear term proportional to a multiplication of displacement and its acceleration is studied. Furthermore, this term is assumed to be small such that the perturbation methods can be applied. Using the method of multiple scales, we investigate the steady-state response of the system in the case of primary and secondary resonances (subharmonic and superharmonic resonances). We show that under resonance condition, the steady-state response undergoes jump phenomena, which depends on how close the frequency of the external force to the natural frequency of the system. We also present approximate analytical solution using the multiple scales method and its numerical solution. Both are in good agreement. Keywords: Weakly Nonlinear Oscillators, Multiple Scales, Perturbation Methods Share Link | Plain Format | Corresponding Author (Farrell Theodore Adriano)

217	MATHEMATICS AND STATISTICS	ABS-36
INTERVAL ESTIMATION OF NONPARAMETRIC REGRESSION CURVE FOURIER SERIES (Case Study Data of Poverty in East Java Province 2021) Idrus Syahzaqi (a*), Jerry Dwi Trijoyo Purnomo (a), I Nyoman Budiantara (a) a) Department of Statistics, Institut Teknologi Sepuluh Nopember, Surabaya, 60111, Indonesia * idrus.syahzaqi[at]gmail.com Abstract Regression is one of the analytical methods used to determine the relationship pattern between response variables and predictor variables. There are three approaches used in regression, namely parametric, nonparametric, and semiparametric regression. When the data used is not known the shape of the regression curve, then the nonparametric regression approach can be an option. In addition, the nature of flexibility in nonparametric regression can be seen by setting certain criteria, for example the presence of optimal oscillations in the nonparametric Fourier series regression, then the data will determine the shape of the estimation of the regression curve, without being influenced by the subjectivity factor of the researcher. Research using nonparametric regression has been carried out a lot. However, from several studies that have been conducted, there are still not many studies that examine interval estimation in the nonparametric regression estimator of the Fourier Series. The interval estimation for the nonparametric regression curve of the Fourier series estimator has the advantage of having a smaller error probability value than point estimation because it is not focused on one point but is based on a range of the highest (max) and lowest (min) values. The application of interval estimation can be applied to various fields of science, including in the field of economics in the case of poverty. East Java Province was chosen as the object of research, considering that this region occupies the first position with the highest poverty rate in Indonesia. This research aims to estimate the nonparametric Fourier series regression interval that is applied to the percentage of poverty in East Java Province. The function used in the nonparametric regression estimator of the Fourier Series is the cos function. The method used to determine the optimum number of oscillation parameters in the Fourier Series uses the minimum Generalized Cross Validation (GCV) value. Keywords: Interval Estimation, Nonparametric Regression, Fourier Series, Percentage of Poverty Share Link | Plain Format | Corresponding Author (Idrus Syahzaqi)

218	MATHEMATICS AND STATISTICS	ABS-297
Interval Estimations for Parameters of Bathtub Hazard Model with Fixed Covariate in the Presence of Right- Censored Data Idari Ismail(a*,b), Assoc. Prof. Dr Jayanthi Arasan(a), Dr Mohd Shafie Mustafa(a), Dr Muhammad Aslam Mohd Safari(a) a) Department of Mathematics and Statistics, Faculty of Science Universiti Putra Malaysia (UPM) 43400 UPM Serdang Selangor Darul Ehsan MALAYSIA *idari512[at]uitm.edu.my b) Mathematical Sciences Studies, College of Computing, Informatics and Media, Universiti Teknologi MARA (UiTM) Cawangan Kelantan, 18500 Machang, Kelantan Darul Naim MALAYSIA Abstract In this study, a two-parameter lifetime model has been extended to incorporate covariate in the presence of right-censored data. The model has bathtub-shaped or increasing failure rate function which enables it to fit real lifetime data sets. The method of maximum likelihood was used to estimate the parameters in the model and a simulation study was then conducted to evaluate the performance of parameter estimates at various sample sizes and censoring proportion levels. The results from simulation study show that larger sample sizes and smaller censoring proportion give better estimates. Further, three interval estimation methods: Wald, likelihood ratio and bootstrap-t (B-t) were constructed, and the performance of these methods was evaluated based on a coverage probability study. Both Wald and likelihood ratio techniques appear to have better performance when the sample size is larger. On the other hand, B-t method performs better than those two techniques at smaller sample sizes. Finally, an application to a real medical data is presented for illustrative purposes. Keywords: bathtub-shaped- right-censored- interval estimation method Share Link | Plain Format | Corresponding Author (IDARI ISMAIL)

219	MATHEMATICS AND STATISTICS	ABS-47
Revisiting Kantorovich Operators in Lebesgue Spaces Maximillian Ventura Obie Welly, Erick Angga Taebenu, Reinhart Gunadi, Denny Ivanal Hakim Institut Teknologi Bandung Abstract According to the Weierstrass Approximation Theorem, any continuous function on the closed and bounded interval can be approximated by polynomials. A constructive proof of this theorem uses the so-called Bernstein polynomials. For the approximation of integrable functions, we may consider Kantorovich operators as certain modifications for Bernstein polynomials. In this paper, we investigate the behavior of Kantorovich operators in Lebesgue spaces. We first give an alternative proof of the uniform boundedness of Kantorovich operators in Lebesgue spaces by using the Riesz-Thorin Interpolation Theorem. In addition, we examine the convergence of Kantorovich operators in the space of essentially bounded functions. We also consider the rate of convergence of Kantorovich operators in some subspaces of Lebesgue spaces. Keywords: Kantorovich operators, Lebesgue spaces, interpolation of linear operators Share Link | Plain Format | Corresponding Author (Maximillian Ventura Obie Welly)

220	MATHEMATICS AND STATISTICS	ABS-48
On Ramsey number for tree versus kipas graph of odd order Intan Sherlin (a), Suhadi Wido Saputro (b), Edy Tri Baskoro (b,c*) (a) Doctoral Program of Mathematics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia 30121002[at]mahasiswa.itb.ac.id (b) Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia suhadi[at]itb.ac.id (c) Center for Research Collaboration on Graph Theory and Combinatorics, Indonesia *ebaskoro[at]itb.ac.id Abstract Given two graphs G and H, the graph Ramsey number R(G, H) is the least natural number r such that for every graph F on r vertices, either F contains a copy of G or \overline{F} contains a copy of H. A vertex v is called a dominating vertex in a graph G if it is adjacent to all other vertices of G. A wheel W_n is a graph consisting one dominating vertex and n other vertices forming a cycle. A kipas F_{1,m} is a fan graph formed from a wheel W_n by removing one cycle-edge. In this paper, we consider the graph Ramsey number of a tree T_n and a kipas F_{1,m}. The study of R(T_n,F_{1,m}) has been initiated by Li et. al. (2016) where T_n is a star. This paper will give the graph Ramsey numbers for T_n is not a star versus kipas F_{1,m} with m=4, 6, and 8. Keywords: graph Ramsey number, Ramsey number tree versus kipas Share Link | Plain Format | Corresponding Author (Intan Sherlin)

221	MATHEMATICS AND STATISTICS	ABS-308
On the Spectrum of Laplace Operator Defined on the Metric Graphs of Platonic Solids Hendri Maulana, Yudi Soeharyadi*, Oki Neswan Faculty of Mathematics and Natural Science, Bandung Institute of Technology Jalan Ganesha 10, Bandung 40132, Indonesia *ysoeharyadi[at]itb.ac.id Abstract A metric graph is a graph, for which each of the edge is identified with a finite interval. The length of the interval is interpreted as the weight of the edge. In order for a set of functions on the edges of a metric graph is considered to define a function on the whole graph, conditions on each vertex must be imposed. Some of the most common vertex conditions are continuity condition and Kirchhoff condition. In this study we report on the eigenvalues of the Laplace operator defined on the metric graphs of the Platonic Solids. Laplacian eigenvalue problem on metric graphs is described in a second order ordinary differential equation with Kirchhoff condition of vertices. Specifically, we discuss the algorithm for determining the eigenvalues of the Laplace operator by implementing calculations for two simplest platonic solids, namely the tetrahedron graph and the cube graph. We assume that the length the edges is uniform. Keywords: Spectrum Laplace operator, Metric platonic solid graph, Continuity conditions, Kirchhoff condition Share Link | Plain Format | Corresponding Author (Hendri Maulana)

222	MATHEMATICS AND STATISTICS	ABS-53
Logistic Regression Approach with Rare Event Weighted Logistic Regression and Majority Weighted Minority Oversampling Technique for Imbalanced Data (Case Study: Child Participation in Economic Activities in Southeast Sulawesi) Regina Hayden Sagita (a*), Ismaini Zain (a), Vita Ratnasari (a) a) Statistics Department, Institut Teknologi Sepuluh Nopember Jl. Arief Rahman Hakim, Surabaya 60111 Indonesia *reginahaydensagita[at]gmail.com Abstract Indonesia is one of the countries with a fairly high number of child workers. The Central Bureau of Statistics recorded 1.17 million people aged 10-17 years working in the country in 2020 with an ever-increasing percentage. The highest child labor data in Indonesia was recorded in the Southeast Sulawesi region. According to Susenas data, for ages 10-14 years, there was 4.89 percent child labor. Child labor is closely related to poverty, meaning that family environmental factors and education level are determinants of childrens participation in economic activities. Classification is the process of finding a set of models with the aim that these models can be used to predict the class of an object or data. The problem in data classification is the composition of imbalanced data. In binary classification or two classes, one class has a larger number of samples than the other class, so this study will apply the Rare Event Weighted Logistic Regression (RE-WLR) and Majority Weighted Minority Oversampling Technique (MWMOTE) methods. The case of the level of participation of children in the economy, namely, among the proportion of children aged 10-14 years who work in 2019 shows this case is included in the imbalanced data category. The main topic of this study is how the results of the comparison of the RE-WLR and MWMOTE methods as well as the socio-economic conditions of families affect the status of child labor in the family, to find out what child workers are that affect the level of child labor in Southeast Sulawesi, so that the influential indicators can be addressed in order to reduce the number of workers child. The results show that the factors that influence child labor are the child age, sex of the child, schooling status of the child, age of the head of the household, gender of the head of the household, location of residence, business field of the head of the household, and employment status of the head of the household. Keywords: Child Labor- Imbalanced- RE-WLR- MWMOTE Share Link | Plain Format | Corresponding Author (Regina Hayden Sagita)

223	MATHEMATICS AND STATISTICS	ABS-54
On Multiplicative Circulant Networks of Order Power of Two: Breadth-first Search Tree, Diameter, Distance Spectral Radius, Forwarding Indices, and Some Distance-based Topological Indices John Rafael M. Antalan \(^{1,2}\) and Francis Joseph H. Campena \(^2\) \(^1\)Department of Mathematics and Physics, College of Science, Central Luzon State University, Science City of Munoz, Nueva Ecija, Philippines \(^2\)Department of Mathematics and Statistics, College of Science, De La Salle University, 2401 Taft Ave., Malate, Manila, Philippines Abstract Let \(G\) be a group with identity element \(e\), and assume \(S\subseteq G-\{e\}\). Recall that the graph \(\Gamma\) with \(V(\Gamma)=G\) and \(E(\Gamma)=\{\{g,sg\}:g\in G\ \mbox{and}\ s\in S \}\) is the well-known Cayley graph with connection set \(S\). If our Cayley graph is such that \(G=<\mathbb{Z}_n,+_n>\), then we have a circulant network. Now, let \(m>1\) and \(h\geq 0\) be integers. The graph with vertex set \(\{0,1,...,m^h-2,m^h-1\}\) and edge set \(\{\{u,v\}:\mbox{either}\ u+v\equiv s(mod\ m^h )\ \mbox{or}\ u-v\equiv s(mod\ m^h )\} \) where \(s\in S=\{m^0,m^1,...,m^{h-1}\} \) is called multiplicative circulant network of order \(m^h\) and is denoted by \(MC(m^h)\). Thus, multiplicative circulant networks are special type circulant networks where \(G=\mathbb{Z}_{m^h}\) and \(S=\{m^0,m^1,...,m^{h-1}\}\). Multiplicative circulant networks and circulant networks in general are applied in computer network design, telecommunication networking, and distributed computation. In this study, we provide a method in constructing the breadth-first search tree (BFS tree) of \(MC(2^h)\). We then use the constructed BFS tree to compute for some important network properties of \(MC(2^h)\) such as the diameter, distance spectral radius, forwarding indices, and some distance-based topological indices. The provided method in constructing the BFS tree for \(MC(2^h)\) in this study paves an easy way in determining the distance spectral radius, forwarding indices, and some distance-based topological indices of \(MC(2^h)\). Finally, the computed diameter for \(MC(2^h)\) using the method presented in this study agrees with the diameter computed by Arno and Wheeler (1993). Keywords: network, circulant networks, multiplicative circulant networks, breadth-first search tree, diameter, forwarding index, topological index Share Link | Plain Format | Corresponding Author (John Rafael Macalisang Antalan)

224	MATHEMATICS AND STATISTICS	ABS-55
Improving the Forecasting of Car Sales using a Hybrid of Time Series Regression and Support Vector Regression with Google Trend Indices as Additional Predictors Reny Dyah Puspitasari (a*), Dedy Dwi Prastyo (b) a) Interdisiplinary School of Management and Technology, Institut Teknologi Sepuluh Nopember, Surabaya, 60111, Indonesia *Correspondence, email: reny.dyah[at]gmail.com b) Department of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Surabaya, 60111, Indonesia e-mail: dedy-dp[at]statistika.its.ac.id Abstract The automotive industry is a leading sector that significantly contributes to the national economy. During the COVID-19 pandemic, there was a decrease in annual car sales by up to 40%, even a decrease in monthly car sales in May 2020 by up to 81,8%. On the other hand, car sales may relate with the searching behavior of internet users before they buy the car. The high growth of internet users in Indonesia recently, which has reached 210 million users, plays a significant role in people^s behavior for seeking information online before buying products. Google has summarized this search traffic for particular terms into the so-called Google Trend index. This research utilizes the Google Trend indices of chosen terms as additional predictors to improve the forecasting performance of car sales. This research performs car sales forecasting model by combining linear and non-linear models through two modeling stages. The first step employs Time Series Regression (TSR) with dummy variables to accommodate the trends patterns, seasonality, and calendar variations pattern. In the second step, the non-linear model Support Vector Regression (SVR) is employed to model the residual of TSR. In addition, the Google Trend indices are used as additional predictors during the modeling TSR in the first step. The involvement of Google Trend indices in the model, along with the hybrid approach, is expected to improve forecasting accuracy. Keywords: Car Sales Forecasting, Google Trends, Hybrid Model, Time Series Regression, Support Vector Regression Share Link | Plain Format | Corresponding Author (Reny Dyah Puspitasari)

225	MATHEMATICS AND STATISTICS	ABS-314
Trees with Distinguishing Number Three Andi Pujo Rahadi (a), Edy Tri Baskoro (b*), Suhadi Wido Saputro (c) a), b), c) Center for Research Collaboration on Graph Theory and Combinatorics a), b), c) Institut Teknologi Bandung *ebaskoro[at]itb.ac.id Abstract Let G(V,E) be a simple connected graph with the vertex-set V and the edge-set E. A vertex k-labeling on G is a mapping f from V(G) onto {1,2,..., k}. The distinguishing number of G, denoted by D(G), is the least natural number k such that G has a vertex k-labeling that is preserved only by the trivial automorphism. In this talk, we characterize all trees of radius two with the distinguishing number three. Keywords: distinguishing number- graph automorphism- tree Share Link | Plain Format | Corresponding Author (Andi Pujo Rahadi)

226	MATHEMATICS AND STATISTICS	ABS-316
On The Double Newton Method for Solving Fuzzy Quadratic Linear Control Form Zani Anjani Rafsanjani Hsm (a,b)*, Hilal Akmal Almubarok Perdana Adiputra (b), Sugiyarto Surono (b) (a) Department of Mathematics, Faculty of Science and Mathematics, Diponegoro University, Semarang, Indonesia *zani.anjani4[at]gmail.com, zani[at]lecturer.undip.ac.id (b) Department of Mathematics, Faculty of Science and Applied Technology, Ahmad Dahlan University, Yogyakarta, Indonesia Abstract Quadratic linear control is a mathematical system of equations modeled from various life phenomena. However, there are numerous problems associated with the process of optimizing linear quadratic control in real life, such as the inability to express the variables numerically. We provide a different way to solve the system using fuzzy logic transformation to determine the optimal solution of quadratic linear controls. The dynamic control system consist of the linear performance index and a quadratic constraint. This system transformed with Triangular Fuzzy Number, which formed a multi-objective optimization model. Furthermore, the optimal control function can be determined with some calculation. Hance, to find the optimal solution of the system, the Lyapunov functions will be solved using some numerical methods. In this case, we modify the original Newton Methods and Double Newton Method for the Quadratic Linear Control Fuzzy form. Some numerical examples are given to show the effectiveness of the algorithms. The results shows that The Newton Method and The Double Newton methods gives a good performance to find the optimal control Keywords: fuzzy quadratic control- newton method- double newton method Share Link | Plain Format | Corresponding Author (Zani Anjani Rafsanjani HSM)

227	MATHEMATICS AND STATISTICS	ABS-61
Parameter Estimation and Hypothesis Testing on Geographically & Temporally Weighted Bivariate Log-Normal Regression Models Sindi Wahyu Pratiwi (a*), Purhadi (b), Bambang Widjanarko Otok (b) Department of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Kampus ITS-Sukolilo, Surabaya 60111, Indonesia Abstract Bivariate Log-Normal Regression (BLNR) is a regression with two correlated response variables and log-normal distribution. This model produces global parameter estimates for the entire observation area. In its development, many cases require information from panel data. Panel data can provide more complete information because it covers several periods. The use of the BLNR model on panel data with the observation unit an area is not appropriate because it allows for spatial and temporal heterogeneity. Geographically and Temporally Weighted Bivariate Log-Normal Regression (GTWBLNR) considers spatial and temporal heterogeneity in bivariate regression with log-normal distributed response variables. This study aims to obtain parameter estimators and statistical tests for the GTWBLNR model. Parameter estimation using Maximum Likelihood Estimation (MLE) with Newton Raphson numerical iteration. Test statistics for simultaneous testing using the Maximum Likelihood Ratio Test (MLRT) method, for large sample size, the distribution of the test statistics G^{2} approaches Chi-Square. Meanwhile, the partial testing is derived from a central limit theorem which results in Z test statistic. Keywords: Log-Normal Distribution-GTWBLNR-MLE-MLRT. Share Link | Plain Format | Corresponding Author (Sindi Wahyu Pratiwi)

228	MATHEMATICS AND STATISTICS	ABS-62
Time Series Intervention Analysis on Count Data of Foreign Tourist Arrivals with Log-Linear Poisson AR and Poisson Autoregressive (PAR(p)) Veniola Forestryani (a) , Hidayatul Khusna (b*), Agus Suharsono (c) a) Department of Statistics, Institut Teknologi Sepuluh Nopember, Surabaya 60111, Indonesia fveniola[at]gmail.com b) Department of Statistics, Institut Teknologi Sepuluh Nopember, Surabaya 60111, Indonesia *hidayatul[at]its.ac.id b) Department of Statistics, Institut Teknologi Sepuluh Nopember, Surabaya 60111, Indonesia agus_s[at]statistika.its.ac.id Abstract Number of foreign tourist arrivals data are count time series containing discrete values in the form of event data, which may follow the Poisson distribution. This type of count data is modeled using time series models like Log-Linear Poisson Autoregressive and Poisson Autoregressive (PAR(p)). The Log-Linear Poisson Autoregressive was developed using the GLM (Generalized Linear Model) method, while PAR(p) was developed using a state-space technique. Number of inputs known as interventions, such as natural disasters, pandemics and its supporting policy, have impacts on foreign tourist arrivals. The first goal of this study is to compare the three methods-Gaussian-AR, Log-Linear Poisson AR, and PAR(p)-to be used for forecasting and examining the effects of the interventions on the number of foreign tourists entering Indonesia through Ngurah Rai Bali Airport. The next goal is to calculate the potential loss that may be incurred based on the best method. COVID-19 pandemic is used as the main intervention in this paper. By contrasting the AIC, RMSE, MAD and MAPE values for each candidate model, Log-Linear Poisson AR was chosen as the model that best fits the data. According to the model, COVID-19 has been discovered to considerably reduce the number of tourists arriving at the Ngurah Rai Airport by 96.4% on average. The estimated values of potential losses due to the presence of COVID-19 pandemic intervention are determined to be 6,890,932,320.99 US dollars in the 2020-2021 biennium based on the monthly tourist expenditures per visit in the year of 2019. Keywords: Intervention analysis, Log-linear Poisson AR, PAR(p), Foreign tourist arrivals, COVID-19 Share Link | Plain Format | Corresponding Author (Veniola Forestryani)

229	MATHEMATICS AND STATISTICS	ABS-319
SVEIAR: Covid-19 Epidemic Model with Vaccination and Mudik Tradition in Indonesia Darsih Idayani (a*), Asmara Iriani Tarigan (a), Selly Anastassia Amellia Kharis (a), Heny Kurniawati (b) a) Mathematics Program Study, Universitas Terbuka b) Biology Program Study, Universitas Terbuka Abstract The SARS-CoV-2 coronavirus, also called Covid-19, spread to many countries in January 2020 from Hubei Province, PRC. In Indonesia, the first case of Covid-19 occurred in early March 2020. The government has done many things to prevent the spread of Covid-19, urging people to stay at home and carry out regional quarantine and vaccinations. However, the condition of Indonesian society is very complex. The existence of the mudik tradition that is carried out every year by Indonesian people is troubling the government because it risks increasing the spread of the Covid-19 virus. Furthermore, it is difficult for the government to predict the change of infected, dead, and recovered people. Therefore, we proposed an epidemic model for the spread of Covid-19, considering vaccination and mudik traditions, i.e. SVEIAR model. Then the disease-free and endemic equilibrium point and their stability was determined. Keywords: Covid-19- epidemic model- vaccination- mudik tradition Share Link | Plain Format | Corresponding Author (Darsih Idayani)

230	MATHEMATICS AND STATISTICS	ABS-64
Detecting Changepoints in The Stocks Portfolio Using Bayesian Preference with Lag Julius Susanto, Sapto Wahyu Indratno Institut Teknologi Badung Abstract In early 2020, the Covid-19 virus began to spread throughout the world. As a result, the government was forced to make social restrictions mandatory on national and international scales, and the economy started to collapse. Many companies are experiencing losses from this incident which impacts their share price, so the price shares experience a behaviour change. This case example is one case of changes in stock price behaviour due to regulatory changes. When a change occurs in a company that has a significant impact, the difference in stock price behaviour can be seen in the stock price plot. But there are times when change behaviour changes little by little, so it is challenging to know the changepoints. So, there is a need for a method to detect the changepoints in stock price behaviour so that investors can think about the following action to be taken. One of the methods to detect the point of changepoints in time series online data, like stocks, is Bayesian online changepoint detection or EXO. This method can predict the location of the changepoints of time series data that increases over time (online). This method can detect the time of change behaviour quickly, but the result of this method could be more stable. Therefore, this paper will use the lagged exact online Bayesian changepoint form for detection or LEXO. This method incorporates an advanced recursive algorithm with past information, and a recursive algorithm backtracks from the information in the future. Knowing some fore before the decision is hoped that this method^s accuracy will be better than the EXO method. This study will apply the EXO and LEXO methods to multivariate data. It is expected that the EXO and LEXO methods can detect the change points caused by changes in covariance. By knowing the changes in the covariance of stock data, investors can see how good their stock portfolio is. So that drawing conclusions, investors become more thorough. Therefore the normal multivariate model will be used because, according to the simple stock price movement model, the natural logarithm of the geometric stock price returns is normally distributed. In addition, the LEXO method this model will also use to detect skewed data and stock price data with natural logarithms of geometric returns not normally distributed multivariate. Keywords: Bayesian Inference, Changepoints Detection, Simple Stock Price Movement Model, Multivariate Time Series Data Analysis, BOCPD, EXO, LEXO Share Link | Plain Format | Corresponding Author (Julius Susanto)

231	MATHEMATICS AND STATISTICS	ABS-320
On Conditions for Controllability and Local Regularity of a System of Differential Equations Ahmad Hadra Zuhri, Yudi Soeharyadi, Jalina Widjaja Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology Jalan Ganesha 10, Bandung 40132, Indonesia Abstract We consider a system of differential equation on a Banach space \(X\) given by: \begin{equation*} \frac{d}{dt}x(t)=Ax(t)+u(t)f(t,x(t)), x(0)=x_0, \end{equation*} where \(A\) is an infinitesimal generator of a \(C_0\)-semigroup, \(f:R_0^+ \times X \rightarrow X\) is a locally Lipschitz function, and \(u \in L^p ([0,T],R)\) is a control defined on \([0,T]\) with \(1<p<\infty\). Using compactness principle and the generalization of Gronwalls Lemma, the system is shown to be controllable when \(f\) is bounded by a quadratic function. Another result of this study is to examine the local existence and the uniqueness of the solution of the given equation for locally bounded function \(f\) through weighted \(\omega\)-norm. Examples related to the results of this study will be given. Keywords: Differential Equation, Controllability, Local Existence Share Link | Plain Format | Corresponding Author (Ahmad Hadra Zuhri)

232	MATHEMATICS AND STATISTICS	ABS-65
Application of Inverse of Autocovariance Matrix Method on Multivariate GSTAR (MGSTAR) Model For Predicting Economic Variable Data in Java Island Widhiya Nurqisthina Fadhila, Utriweni Mukhaiyar, Sandy Vantika, Gantina Rachmaputri Institut Teknologi Bandung Abstract At the end of 2022, the impact of inflation will be increasingly felt. Prices of essential commodities have increased over time, and some countries have even experienced economic difficulties due to inflation. Sooner or later, inflation will affect farmers purchase prices, thereby worsening the welfare of the community with farmers livelihoods. This problem motivates to conduct research and forecasts related to inflation and farmers exchange rates so that the government can take appropriate actions to minimize possible economic risks. Inflation and farmers exchange rates are monthly time series data which are suspected to be influenced by location, so a space-time model is needed to carry out the analysis. The models commonly used to perform space-time analysis are the STAR and GSTAR models. However, these models can only be used to analyze time series data with one variable at several locations. In this research, the development of the GSTAR model will be used, which can combine many variables in many areas, namely the Multivariate GSTAR (MGSTAR) model. In making predictions, the space-time model must comply with the assumption of stationarity. The stationarity of space-time processes uses the principle that a process has a constant mean and variance throughout the observation time. Just like the GSTAR model, the MGSTAR model can also be defined as stationary by utilizing the VAR form of the model. The process is stationary if all the eigenvalues of the autoregressive parameter matrix are inside the unit circle. However, as the time order of the model increases, the characteristic equation will become more complicated, so it will be challenging to find the eigenvalues. In 2012, Mukhaiyar developed a new alternative method for examining the stationarity of the GSTAR model, namely the inverse approach of the autocovariance matrix or IAcM. Adapting from this research, in this study, we will look for IAcM to check the stationarity of the MGSTAR model. The results show that the IAcM method for MGSTAR is similar to the IAcM method for GSTAR. The only difference between the two is that the IAcM for the MGSTAR model expands as the number of variables increases. The MGSTAR modelling procedure will be applied to forecast monthly economic data in several provinces in Java, namely West Java, Central Java and East Java, with economic variables consisting of inflation and farmers exchange rates (FER). Parameter estimation using distance inverse weighting in model building is obtained using the OLS method for MGSTAR. After getting a suitable model for inflation and FER data, a diagnostic test will be carried out on the model. In this study, the stationarity diagnostic test of the model will be carried out through an alternative approach, namely, using IAcM on the MGSTAR model. The results of the stationarity check through IAcM will be compared with the stationary check through the eigenvalue approach. The AIC value indicates that the MGSTAR(1-1) and MGSTAR(2-1,1) models have the best autoregressive order in conducting data modelling. Examination through the IAcM approach yields different conclusions from the eigenvalue approach, which says that the two models are stationary. Even so, the forecast results for the MGSTAR(1-1) and MGSTAR(2-1,1) models are pretty good, and this is indicated by the small RMSE values of the two models, namely 1.38 and 1.46. Keywords: Inverse of Autocovariance Matrix (IAcM), Multivariate GSTAR (MGSTAR), inflation, farmers exchange rate, West Java, Central Java, East Java Share Link | Plain Format | Corresponding Author (Widhiya Nurqisthina Fadhila)

233	MATHEMATICS AND STATISTICS	ABS-69
Exponential Fraction Index of Some Interconnection Networks John Rafael M. Antalan, Noel F. Laoang Jr. Department of Mathematics and Physics, College of Science, Central Luzon State University (3120), Science City of Munoz, Nueva Ecija, Philippines Abstract Topological Indices have many applications in theoretical chemistry. It is used to calculate the sum of the shortest path between molecules, determine the total number of independent sets and matchings, and more that is useful in developing quantitative structure-activity relationships (QSAR). As new molecules and more complex graphs evolve, Prakasha and Kiran introduced the Exponential Fraction index (a degree-based index) defined as EF(G)=&#8721-_(uv&#8712-E(G))e^(du/dv) where du and dv are the maximum and minimum degrees, respectively. Moreover, Praksha and Kiran calculated the Exponential Fraction index of double graphs, subdivision graphs, complements of some standard graphs, and the index for chemical structures of Graphene and Carbon nanocones. This paper aims to provide additional results to the emerging topological index. We calculated the Exponential Fraction index of the Honeycomb network, Hexagonal network, Rhombus Oxide network, Regular Triangulate Oxide network, Dominating Oxide network, Regular Triangulate Silicate network, and Dominating Silicate network. Keywords: Exponential Fraction Index, Honeycomb network, Hexagonal network, Rhombus Oxide network, Regular Triangulate Oxide network, Dominating Oxide network, Regular Triangulate Silicate network, Dominating Silicate network Share Link | Plain Format | Corresponding Author (Noel Jr. Fortusa Laoang)

234	MATHEMATICS AND STATISTICS	ABS-325
Estimation of Gompertz, Makeham, and Weibull Distribution Model for Pension Fund Participant Data and Its Comparison with the 2019 Indonesian Mortality Table Utriweni Mukhaiyar*, Arsyad Syahroni, Alma Justica, KhaerunNisa SH, Mukhlisah Actuarial Study Program, Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology, Bandung, 40132, Indonesia *Email: utriweni.mukhaiyar[at]itb.ac.id Abstract This study discusses the estimation of the Gompertz, Makeham, and Weibull distribution models for pension fund participant data and its comparison with the 2019 Indonesian Mortality Table. It is important for pension fund institutions to determine the most appropriate mortality assumptions for their actuarial calculations so that companies can fulfill their responsibilities in providing benefits as promised to participants at the beginning of the coverage period. In this study, researchers took data from 500 female participants and 500 male participants of the pension fund company. Based on the results of the descriptive statistics, it is known the data has negative skewness and kurtosis, which are -1.02 and -0.65 for female participants data, and -0.83 and -0.96 for male participants data. Furthermore, parameter estimation is performed on the three mortality distributions that are often used, namely the Gompertz, Makeham, and Weibull distributions using the Nonlinear Least Square (NLS) method, then the best distribution model is selected to estimate the mortality assumptions from the data of pension fund company participants. The selection of the best distribution is based on the smallest Mean Square Error (MSE) value compared to other distributions. The best distribution for female participants is the Gompertz distribution, while for male participants is the Makeham distribution. After being compared with the mortality table, the results obtained are for female participants, the most appropriate mortality assumption is using the 2019 Indonesian Mortality Table (TMI IV) because the MSE value of TMI IV is smaller than the MSE value of the Gompertz distribution. As for male participants, the mortality assumption is most appropriate using the Makeham distribution approach, because the MSE value of the Makeham distribution is smaller than the MSE value of TMI IV. Keywords: Parameter Estimation, Gompertz, Makeham, Weibull, Pension Fund, Indonesian Mortality Table. Share Link | Plain Format | Corresponding Author (Alma Justica)

235	MATHEMATICS AND STATISTICS	ABS-70
Optimization of Jar Test Process Parameters Using Taguchi and Response Surface Methodology with Desirability Function Approach Hani Brilianti Rochmanto (*a), Muhammad Mashuri (b), Muhammad Ahsan (c) a,b,c) Department of Statistics, Institut Teknologi Sepuluh Nopember, Surabaya 60111, Indonesia *rochmantohani.206003[at]mhs.its.ac.id Abstract The production process of the tofu factory produces wastewater with high levels of organic compound. This compound will reduce water quality if it is discharged directly into the river. This study aims to find the optimal combination of coagulation factor levels so that the waste meets the quality standards before being disposed of or reused. The factors studied included coagulant dosage, agitation speed, agitation time, and settling time. The water result from the jar test process can be measured through these response variables: pH and turbidity levels. Desirability Function (DF) is used to solve multi-response problems, by transforming the two responses into a composite desirability value. The relationship between factors and responses is modelled using second-order Response Surface Methodology (RSM) and Taguchi method, where the goodness of the model is measured based on the largest R2 value, and the smallest Mean Absolute Error (MAE) and Root Mean Square Error (RMSE). The best model obtained will be used to determine the optimal factor level combination in the jar test process, by observing the factors which have a significant effect and the contribution of each factor to the model. The results of the analysis showed that the dose of coagulant, agitation time and speed had a significant effect on the changes in turbidity and pH of the waste. Optimum conditions were obtained at the combination of the coagulant dose of 100 mg, agitation time of 2 minutes, and agitation speed of 100 rpm. Keywords: desirability function, jar test, response surface methodology, taguchi Share Link | Plain Format | Corresponding Author (Hani Brilianti Rochmanto)

236	MATHEMATICS AND STATISTICS	ABS-71
CONSTRUCTING SPECIES-HABITAT NETWORK FOR ANIMAL CONSERVATION Ahmad Shulhany (a), Agus Yodi Gunawan (a,*), Hilda Assiyatun (b), Iding Achmad Haidir (c,d) (a) Industrial and Financial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung. (b) Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung. (b) Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung. (c) Directorate General of Natural Resources and Ecosystem Conservation, Indonesian Ministry of Environment and Forestry, Jakarta, Indonesia. (d) Wildlife Conservation Research Unit, Department of Biology, University of Oxford, Oxford, UK. (*) corresponding author: ayodi[at]itb.ac.id Abstract The relationship between species and habitat is an essential topic in animal conservation. Species live in a habitat that provides food and contributes to the habitat. This relationship can be modelled as a graph with two types of vertices, known as a bipartite graph. Graph G=(V,E) is an ordered pair of the vertex set V and edge set E such that E&#8838-[V]^2. In the habitat species network, vertices represent species or habitats. The vertices representing species are called species vertex sets (V_s), while the vertices representing habitats are called habitat vertex sets (V_h). The edge connecting a species vertex and a habitat vertex is defined as the species visiting that habitat. In this study, we used three similarity indices to describe the condition of several species or habitats in the Bungo area. These similarity indices are structural equivalence, Jaccard similarity, and Pearson correlation coefficient. Keywords: Network, species, habitat, conservation. Share Link | Plain Format | Corresponding Author (Ahmad Shulhany)

237	MATHEMATICS AND STATISTICS	ABS-72
Clique Number and Chromatic Number of the Coprime Graph of the Generalized Quarternion Group Marena Rahayu Gayatri(a*), Amila Ulul Azmi(a), Nurhabibah(a), I Gede Adhitya Wisnu Wardhana(a) a)Department of Mathematics, Faculty of Mathematics and Natural Science, Mataram University, Jalan Majapahit 62, Mataram 83115, Indonesia. *marenarahayu2002[at]gmail.com Abstract Group theory and graph theory are two theories that are often combined in research. The generalized quaternion group is one of the interesting things to study. In this research, we find the clique number and chromatic number of the coprime graph of the generalized quaternion group. The method used is by reading references related to the generalized quaternion group , coprime graphs, clique number, and chromatic number. Results that obtained from this study show that the clique number of coprime graphs as same as the chromatic number of coprime graphs for each case of n. Keywords: Clique number, chromatic number, coprime graphs, generalized quarternion group Share Link | Plain Format | Corresponding Author (Marena Rahayu Gayatri)

238	MATHEMATICS AND STATISTICS	ABS-328
Comparison of Generalized Poisson and Binomial Negative Regression Models in Handling Overdispersion Based on Akaike Information Criterion Darnah 1,*), M.Fathurahman 1), Rut Esra 1), Suyitno1), Memi Nor Hayati 1), Rahmawati Munir2) 1)Statistics Department, Faculty of Mathematics and Natural Science, Mulawarman University, Jl. Barong Tongkok No.4, kampus Gn Kelua, Samarinda, 75123 2)Physics Department, Faculty of Mathematics and Natural Science, Mulawarman University, Jl. Barong Tongkok No.4, kampus Gn Kelua, Samarinda, 75123 *Corresponding author: darnahstat[at]fmipa.unmul.ac.id Abstract Poisson regression analysis is the popular regression model on the discrete response variables, it has an assumption that mean and variance of response variable is equal or equidispersion. However, the count data in pulmonary tuberculosis cases often display the variance value is greater than the mean value or overdispersion. Inappropriate imposition of the Poisson regression may underestimate the standard errors and overstate the significance of the regression parameters, and consequently, giving misleading inference about the regression parameters. This paper suggests the comparison of Generalized Poisson and Negative Binomial regression models as alternatives for handling overdispersion on pulmonary tuberculosis cases in Indonesia in 2021 based on the smallest Akaike Information Criterion (AIC) value. According to the result, AIC values of Binomial Negative regression model is smaller than the Generalized Poisson regression model. Therefore, the Binomial Negative regression model is better than Generalized Poisson regression model in handling overdispersion on the pulmonary tuberculosis cases in Indonesia in 2021. Keywords: AIC, Binomial Negative, GPR, overdispersion, pulmonary tuberculosis cases Share Link | Plain Format | Corresponding Author (Darnah Andi Nohe)

239	MATHEMATICS AND STATISTICS	ABS-329
Prediction Model of Reserve on Pension Fund for Civil Servants of University Academic Employees in Indonesia Novriana Sumarti, Sendari Novia Sriyanto Putri, Annisa Rahmienda Maha, Hasna Khalishfi Yasyfa Industrial and Financial Mathematics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung Abstract The pension fund program is a type of long-term planning that aims to provide the living cost of civil servants after retirement. In Indonesia, the pension fund is calculated based on the latest salary of civil servants. As a consequence, there is an imbalance between the accumulated contributions being collected during the working period, and the pension benefits being paid for the rest of life. It results in an increase in the government^s budget burden to meet the sufficient pension fund. In this research, we propose a model to determine the civil servant pension fund that is based on the average salary of the last 10 years using the Accrued Benefit Cost method. We implement the model to determine the reserve of the pension fund of academic employees of Indonesian public universities. The salary increase of the academic staff of public universities is quite unique because it is heavily dependent on individual achievement during the working period. They could retire at age of 65 or 70, which is dependent on their rank. The first step in this study is to build a model to predict the final ranks of employees, which are commonly quite diverse. The regression model will then be used to forecast the percentage of salary increases. The Accrued Benefit Cost method is used to calculate pension benefits, which include salary increases between groups, periodic salary increases, and salary increases based on government regulations. The final step is to forecast the pension fund amount that the government must provide for the public university over the next 20 years, which is taking into account predictions for the final rank of civil servants, salary increase percentages, and potential new civil servants. The data set of new civil servants is created using the Poisson distribution, where the parameter values are obtained by analyzing sample data of civil servants from the past 30 years. In this study, the result of the model shows a significantly lower value than the results of the existing method based on the latest salary. This concludes that the method can reduce the fund amount that must be prepared by the government so that the burden on the state budget could be decreased. Keywords: Reserve, pension fund, time series, prediction model Share Link | Plain Format | Corresponding Author (Novriana Sumarti)

240	MATHEMATICS AND STATISTICS	ABS-75
Classification of the Geochemical Composition of Metorite of Punggur (Astomulyo) by K-Nearest Neighbor Algorithm Triyana Muliawati (a*) a) Department of Mathematics, Institut Teknologi Sumatera Jalan Terusan Ryacudu, Lampung 35365, Indonesia *triyana.muliawati[at]ma.itera.ac.id Abstract The fall of a meteorite in Astomulyo Village, Punggur, Lampung Province in early 2021 is an interesting topic for further study. This rare object has been suggested to have a unique geochemical composition and a special connection with other meterorites. We aimed to trace its classification by comparing it with other well-known meteorites that have been studied previously. We approach the classification process using the k-nearest neighbor algorithm. The database used represents the geochemical data for each known meteorite group. As a result, we clearly identified that with a k-value = 5 and the proportion of test data 5/95 (in %), the geochemical composition of this meteorite is relatively close to that of the H-type chondrite group with a value accuracy of 91.67%. These results are consistent with the fact that the meteorite of Punggur has a high total iron and metallic composition. Keywords: Meteorite- K-Nearest Neighbor- Geochemistry- Astomulyo Share Link | Plain Format | Corresponding Author (Triyana Muliawati)

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